Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A

Average Error: 0.1 → 0.1

Time: 23.1s

Precision: 64

Math

\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]

↓

\[\left(y + x\right) + \left(\frac{1 - \log t \cdot \log t}{1 + \log t} \cdot z + \left(a - 0.5\right) \cdot b\right)\]

C

double f(double x, double y, double z, double t, double a, double b) {
        double r21036998 = x;
        double r21036999 = y;
        double r21037000 = r21036998 + r21036999;
        double r21037001 = z;
        double r21037002 = r21037000 + r21037001;
        double r21037003 = t;
        double r21037004 = log(r21037003);
        double r21037005 = r21037001 * r21037004;
        double r21037006 = r21037002 - r21037005;
        double r21037007 = a;
        double r21037008 = 0.5;
        double r21037009 = r21037007 - r21037008;
        double r21037010 = b;
        double r21037011 = r21037009 * r21037010;
        double r21037012 = r21037006 + r21037011;
        return r21037012;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r21037013 = y;
        double r21037014 = x;
        double r21037015 = r21037013 + r21037014;
        double r21037016 = 1.0;
        double r21037017 = t;
        double r21037018 = log(r21037017);
        double r21037019 = r21037018 * r21037018;
        double r21037020 = r21037016 - r21037019;
        double r21037021 = r21037016 + r21037018;
        double r21037022 = r21037020 / r21037021;
        double r21037023 = z;
        double r21037024 = r21037022 * r21037023;
        double r21037025 = a;
        double r21037026 = 0.5;
        double r21037027 = r21037025 - r21037026;
        double r21037028 = b;
        double r21037029 = r21037027 * r21037028;
        double r21037030 = r21037024 + r21037029;
        double r21037031 = r21037015 + r21037030;
        return r21037031;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Target

Original	0.1
Target	0.3
Herbie	0.1

\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

Derivation

1. Initial program 0.1

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
2. Using strategy rm

3. Applied associate--l+ 0.1

   \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b\]

4. Applied associate-+l+ 0.1

   \[\leadsto \color{blue}{\left(x + y\right) + \left(\left(z - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\right)}\]

5. Taylor expanded around inf 0.1

   \[\leadsto \left(x + y\right) + \color{blue}{\left(\left(a \cdot b + \left(z \cdot \log \left(\frac{1}{t}\right) + z\right)\right) - 0.5 \cdot b\right)}\]

6. Simplified 0.1

   \[\leadsto \left(x + y\right) + \color{blue}{\left(\left(1 - \log t\right) \cdot z + b \cdot \left(a - 0.5\right)\right)}\]
7. Using strategy rm

8. Applied flip-- 0.1

   \[\leadsto \left(x + y\right) + \left(\color{blue}{\frac{1 \cdot 1 - \log t \cdot \log t}{1 + \log t}} \cdot z + b \cdot \left(a - 0.5\right)\right)\]

9. Simplified 0.1

   \[\leadsto \left(x + y\right) + \left(\frac{\color{blue}{1 - \log t \cdot \log t}}{1 + \log t} \cdot z + b \cdot \left(a - 0.5\right)\right)\]

10. Final simplification 0.1

    \[\leadsto \left(y + x\right) + \left(\frac{1 - \log t \cdot \log t}{1 + \log t} \cdot z + \left(a - 0.5\right) \cdot b\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))